Orthodontic repositioning appliances having improved geometry, methods and systems

ABSTRACT

The present invention provides methods and systems including orthodontic tooth positioning appliances. An exemplary appliance can include teeth receiving cavities shaped such that, when worn by a patient, repositioning the patient&#39;s teeth from a first arrangement toward a subsequent or target arrangement. Appliances can include a cavity having one or more shaped features or protrusions shaped and/or positioned so as to apply a desired force to a patient&#39;s tooth received in the cavity and move the tooth along a desired path or direction.

CROSS-REFERENCE TO RELATED APPLICATION

The present invention claims the benefit of priority under 35 U.S.C.§119(e) of U.S. Provisional Application No. 61/024,536, filed Jan. 29,2008 (Attorney Docket No. 018563-014400US), the entire content of whichis incorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to the field of orthodontics,and more particularly to dental repositioning appliances having improvedor optimized geometries incorporating one or more shaped features orprotrusions.

An objective of orthodontics is to move a patient's teeth to positionswhere function and/or aesthetics are optimized. Traditionally,appliances such as braces are applied to a patient's teeth by anorthodontist or dentist and the set of braces exerts continual force onthe teeth and gradually urges them toward their intended positions. Overtime and with a series of clinical visits and adjustments to the braces,the orthodontist adjusts the appliances to move the teeth toward theirfinal destination.

More recently, alternatives to conventional orthodontic treatment withtraditional affixed appliances (e.g., braces) have become available. Forexample, systems including a series of preformed aligners have becomecommercially available from Align Technology, Inc., Santa Clara, Calif.,under the tradename Invisalign® System. The Invisalign® System isdescribed in numerous patents and patent applications assigned to AlignTechnology, Inc. including, for example in U.S. Pat. Nos. 6,450,807, and5,975,893, as well as on the company's website, which is accessible onthe World Wide Web (see, e.g., the url “align.com”). The Invisalign®System includes designing and/or fabricating multiple, and sometimesall, of the aligners to be worn by the patient before the aligners areadministered to the patient and used to reposition the teeth (e.g., atthe outset of treatment). Often, designing and planning a customizedtreatment for a patient makes use of computer-based 3-dimensionalplanning/design tools, such as software technology available from AlignTechnology, Inc. The design of the aligners can rely on computermodeling of a series of planned successive tooth arrangements, and theindividual aligners are designed to be worn over the teeth andelastically reposition the teeth to each of the planned tootharrangements.

Orthodontic appliances, in general, apply force and torque on a toothcrown to move teeth, with the applied force typically normal withrespect to the surface of a tooth or attachment positioned on the tooth.The tooth root and/or other anatomical structures may hinder the desiredtooth movement and render the center of resistance down below thegingival line and in the tooth bone socket, which can make certainmovements difficult to accomplish by application of force to the toothcrown. If a translational movement is desired, for example, thetranslational force is optimally applied through the center ofresistance or with sufficient counterbalancing forces, otherwise forceon the tooth crown by an appliance can cause unwanted torque withrespect to the center of resistance. Clinically, the unwanted torque canresult in unwanted tooth movement and root movement, thereby decreasingthe effectiveness of the treatment. As appliances are designed tocontact and apply forces to the crown of the tooth, and the tooth centerof resistance lies below the gingival line, applying forces moredirectly about the center of resistance is difficult with existingappliances. Accordingly, improved appliances and techniques are neededfor applying more effective tooth movement forces to the teeth duringorthodontic treatment, and reducing unwanted tooth movements.

SUMMARY OF THE INVENTION

The present invention provides improved orthodontic appliances andrelated methods for more effectively applying tooth moving forces andrepositioning teeth into a desired arrangement. Appliances of theinvention include repositioning appliances having improved or optimizedgeometries incorporating one or more shaped features or protrusions.

In one aspect, the present invention provides methods and systems,including an appliance having teeth receiving cavities shaped such that,when worn by a patient, apply a repositioning force to move thepatient's teeth from a first arrangement toward a subsequent or targetarrangement. Appliances can include a cavity having one or more shapedfeatures or protrusions. Such features or protrusions can be shapedand/or positioned to apply a desired force to a patient's tooth receivedin the cavity so as to more effectively move the tooth along a desiredpath or direction.

For a fuller understanding of the nature and advantages of the presentinvention, reference should be made to the ensuing detailed descriptionand accompanying drawings. Other aspects, objects and advantages of theinvention will be apparent from the drawings and detailed descriptionthat follows.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A illustrates a jaw together with an incremental positioningadjustment appliance according to an embodiment of the presentinvention.

FIGS. 1B-1E illustrate various protrusion configurations andorientations including horizontal continuous ridge (FIG. 1B), verticalcontinuous ridge (FIG. 1C), and discontinuous ridge (FIGS. 1D and 1E),according to several embodiments of the present invention.

FIGS. 2A-2F illustrate positioning of shaped features for buccal-lingualtranslation, according to an embodiment of the present invention.

FIGS. 3A-3D illustrate positioning of shaped features for distal-mesialtranslation, according to an embodiment of the present invention.

FIGS. 4A-4C illustrate positioning of shaped features forextrusion-intrusion movements, according to an embodiment of the presentinvention.

FIGS. 5A-5B illustrate positioning of shaped features for toothrotations, according to an embodiment of the present invention.

FIG. 6A is a flowchart of a process of specifying a course of treatmentincluding a subprocess for calculating aligner shapes in accordance withthe invention, according to an embodiment of the present invention.

FIG. 6B is a flowchart of a process for calculating aligner shapes,according to an embodiment of the present invention.

FIG. 7 is a flowchart of a subprocess for creating finite elementmodels, according to an embodiment of the present invention.

FIG. 8 is a flowchart of a subprocess for computing aligner changes,according to an embodiment of the present invention.

FIG. 9A is a flowchart of a subprocess for calculating changes inaligner shape, according to an embodiment of the present invention.

FIG. 9B is a flowchart of a subprocess for calculating changes inaligner shape, according to an embodiment of the present invention.

FIG. 9C is a flowchart of a subprocess for calculating changes inaligner shape, according to an embodiment of the present invention.

FIG. 9D is a schematic illustrating the operation of the subprocess ofFIG. 5B, according to an embodiment of the present invention.

FIG. 10 is a flowchart of a process for computing shapes for sets ofaligners, according to an embodiment of the present invention.

FIGS. 11A-11B illustrate an initial tooth position with a positioneddental appliance, and a resulting undesirable force vector,respectively, according to an embodiment of the present invention.

FIGS. 11C-11D illustrate a relief addition to the dental appliance tocounteract the undesirable force vector around the tooth, and theresulting desired application of the predetermined force on the tooth bythe dental appliance, respectively, according to an embodiment of thepresent invention.

FIG. 12 illustrates a modified dental appliance geometry including anadditional shape modification to remove a gap between the dentalappliance and the tooth, according to an embodiment of the presentinvention.

FIG. 13 is a flowchart illustrating the optimized shape geometry of thedental appliance, according to an embodiment of the present invention.

FIG. 14 is a flowchart illustrating a process of shape feature designand positioning, according to an embodiment of the present invention.

DETAILED DESCRIPTION

The invention described herein describes systems and methods includingorthodontic appliances having geometries designed to provide moreprecise control of the forces and moments applied to a tooth, therebyproviding better control of the type of tooth movement desired whileavoiding unwanted movements, such as unwanted tipping. Appliancesaccording to the present invention can be designed to include certain“shaped features”, such as shaped protrusions (e.g., ridges, dimples,etc.) positioned in a tooth receiving cavity, incorporated intoappliance design and structure.

Appliances having teeth receiving cavities that receive and repositionteeth, e.g., via application of force due to appliance resiliency, aregenerally illustrated with regard to FIG. 1A. As illustrated, FIG. 1Ashows one exemplary adjustment appliance 10 which is worn by the patientin order to achieve an incremental repositioning of individual teeth inthe jaw 11. The appliance can include a shell (e.g., polymeric shell)having teeth-receiving cavities that receive and resiliently repositionthe teeth. Similar appliances, including those utilized in theInvisalign® System, are described in numerous patents and patentapplications assigned to Align Technology, Inc. including, for examplein U.S. Pat. Nos. 6,450,807, and 5,975,893, as well as on the company'swebsite, which is accessible on the World Wide Web (see, e.g., the url“align.com”). Appliances according to the present invention furtherinclude one or more shaped features disposed in a tooth receiving cavityof the appliance, as further described below. As further describedherein, shapes features can be designed, located and distributed toprecisely control the moments produced on a patient's tooth as theappliance is worn by the patient. Incorporation of such protrusions andshaped features as described herein can advantageously improve designand effectiveness of appliances and clinical results by more preciselyapplying force vectors of necessary magnitude and direction for desiredmovement. Appliances of the present invention having shaped features asdescribed further provide efficient force distribution mechanism thatcan more effectively reduce unwanted force and moment. Furthermore,inclusion of a force driven method of treatment design that focuses onthe causes of tooth movement provides advantages in effectiveness andmovement control compared to existing displacement driven treatmentdesigns.

As set forth in the prior applications, an appliance can be designedand/or provided as part of a set or plurality of appliances. In such anembodiment, each appliance may be configured so that its tooth-receivingcavity has a geometry corresponding to an intermediate or final tootharrangement intended for the appliance. The patient's teeth areprogressively repositioned from their initial tooth arrangement to afinal tooth arrangement by placing a series of incremental positionadjustment appliances over the patient's teeth. The adjustmentappliances can be generated all at the same stage or in sets or batches,e.g., at the beginning of a stage of the treatment, and the patientwears each appliance until the pressure of each appliance on the teethcan no longer be felt. A plurality of different appliances (e.g., set)can be designed and even fabricated prior to the patient wearing anyappliance of the plurality. At that point, the patient replaces thecurrent adjustment appliance with the next adjustment appliance in theseries until no more appliances remain. The appliances are generally notaffixed to the teeth and the patient may place and replace theappliances at any time during the procedure. The final appliance orseveral appliances in the series may have a geometry or geometriesselected to overcorrect the tooth arrangement, i.e., have a geometrywhich would (if fully achieved) move individual teeth beyond the tootharrangement which has been selected as the “final.” Such over-correctionmay be desirable in order to offset potential relapse after therepositioning method has been terminated, i.e., to permit movement ofindividual teeth back toward their pre-corrected positions.Over-correction may also be beneficial to speed the rate of correction,i.e., by having an appliance with a geometry that is positioned beyond adesired intermediate or final position, the individual teeth will beshifted toward the position at a greater rate. In such cases, the use ofan appliance can be terminated before the teeth reach the positionsdefined by the appliance.

Orthodontic appliances, such as illustrated in FIG. 1A, impart forces tothe crown of a tooth at each point of contact between a tooth receivingcavity of the appliance and received tooth. The magnitude of each ofthese forces and their distribution on the surface of the toothdetermines the type of orthodontic tooth movement which results. Typesof tooth movement are conventionally delineated as tipping, translationand root movement. Tooth movement of the crown greater than the movementof the root is referred to as tipping. Equivalent movement of the crownand root is referred as translation. Movement of the root greater thanthe crown is referred to as root movement.

The supporting structures of the tooth offer resistance to movement ofthe tooth. The multitude of resistances offered by the tissues may beconsidered all as one, effectively offering resistance centered about apoint located within the root of the tooth, termed the center ofresistance. A force imparted directly to the center of resistance wouldresult in translation of the tooth. Appliances are often not capable ofproviding force at the center of resistance. A force imparted to thecrown of the tooth can produce a moment about the center of resistancethat results in tipping of the tooth. A second force (and/or additionalforces) applied to the crown of the tooth can be selected produce amoment to counteract the initial moment. If the moment produced by thesecond force is equivalent in magnitude an opposite in direction themoments are cancelled and translation of the tooth is accomplished.Increase of the moment produced by the second force beyond balancing theinitial moment will result in root movement.

For illustrative purposes, three types of tooth movement can beidentified as divisions of a continuum of possible movements. Toothmovements may be in any direction in any plane of space. The presentdisclosure uses the orthodontic convention of delineating movements inthree dimensional space into three classifications: first order, secondorder and third order.

The magnitudes of the forces selected and applied to the teeth, and theproper selection of the locations and distributions on the tooth surfaceupon which they act, are important to controlling the type of toothmovement which is achieved. Previously existing appliance technologydoes not provide for the specific selecting of the location of forceapplication as provided herein, or the calibrated magnitude of force ordetermination of the moments produced by the forces.

In one aspect, the present invention describes appliances having adesign and configuration selected to provide more precise control ofrelationships of the forces and moments applied to a tooth, hence,better controlling the type of tooth movement achieved and increasingthe ability of the aligner to achieve all types of tooth movement (e.g.,first order, second order, third order). In particular, the presentinvention describes incorporation of certain “shaped features” intoappliance design and structure. As further described herein, shapesfeatures can be designed, located and distributed to precisely controlthe moments produced on a patient's teeth as an appliance is worn by thepatient. Any number of shaped features can be utilized for improvedteeth repositioning as described herein. Embodiments described hereincan include features including various shaped protrusions in anappliance cavity (e.g., ridge-like protrusions, dimples, etc.). In oneexample, a combination of shaped features, such as a combination ofattachment-type and non-attachment type (e.g., protrusions) shapedfeatures can be utilized to control the force system produced by anorthodontic appliance.

Shaped features can be incorporated into an appliance design, moreparticularly, design of teeth receiving cavities of an appliance asillustrated above (see, e.g., FIG. 1A). Shaped features can be designedboth in terms of physical/structural features as well as positioningand/or location within a tooth receiving cavity, to distributeappropriate forces in terms of direction and magnitude onto the crown ofthe received tooth. Thus, the force direction and/or force magnitude canbe selected and controlled by positioning the features for contact atdifferent areas or locations on the crown, as well as by the parametersof the feature itself. Exemplary parameters of the shaped featureinclude but are not limited to cross section shape, prominence, length,width, and radius. Shaped features can be integrated with or added tothe existing surfaces of an appliance that is shaped and designed basedon (e.g., matching) the position of the patient's teeth at a subsequentarrangement (e.g., n+1 arrangement).

In another embodiment, however, an appliance surface or cavity featurecan be further modified to compensate for an effect (e.g., appliancedistortion) due to incorporating the shaped feature into the appliancedesign/use. In one embodiment, for example, appliance modification caninclude an altered or inflated appliance surface, where the appliancesurface is modified so as to remove certain forces coming only fromthose features of the appliance in contact with the crown other than theshaped features. Modification in this manner provides optimization ofuse of the shaped features, as well as a precise delivery system forforce and moment only necessary for desired tooth movement.

Various designs, orientations, and/or configurations of shaped featuresare available for use according to the present invention. Shapedfeatures to achieve force profiles favorable to specific types of toothmovement can include both attachment-type features as well asnon-attachment type features. Non-attachment type features can includevarious shaped alterations or protrusions in a surface of an appliance,such as ridges (e.g., interior or exterior), dimples, and the like. Theterms “non-attachment type feature” and “protrusion” (e.g., applianceprotrusion) are typically used interchangeably herein. Dimples includeprotrusions having substantially the same dimensions along a widthcompared to the protrusion length. Ridges, by comparison, includeprotrusions having unequal length and width. Interior protrusions, suchas interior ridges, include a groove or protrusion in an appliance thatrecesses toward an inner surface (e.g., tooth contacting surface) of theappliance, whereas exterior protrusions and ridges bulge toward anexterior surface of the appliance. Protrusion type features, such asdimples and ridges can be either filled with material (e.g., compositematerial) or left unfilled. If it is filled, the composite can becontrolled to solidify after desired shape and/or volume of the filleris obtained. In the following discussion, the general term feature willbe used. But the methods apply on any feature as appropriate.

In some instances, ridge-shaped protrusions may provide differencesand/or advantages for force application compared to other protrusionshapes, such as dimples. For example, dimples having substantially equallength compared to with will typically provide more of a pointapplication of a force to a surface of a tooth. By comparison, aridge-shaped protrusion may allow application force application moreevenly distributed along a surface of a tooth, and may provide moreprecisely controlled tooth movement in some instances. Further,ridge-shaped protrusions by providing more protrusion configuration anddesign options, provide a greater range of force values that can beselected and delivered to the target tooth compared to non-ridge shapes,such as dimples, and can therefore be more likely to impart the desiredload. As such, use of ridges compared to other more simplified shapes(e.g., a single dimple) provide a greater range of available forcevalues or selections for imparting the desired load vector, or forcedirection and/or magnitude along a tooth surface, thereby providing moretreatment options.

As noted, various designs, orientations, and/or configurations of shapedfeatures are available for use according to the present invention andcan depend, at least partially, on the desired application of force andtooth movement. Exemplary designs/configurations of ridged protrusionsare illustrated with reference to FIGS. 1B-1E. FIG. 1B illustrates aridge 12 formed by a continuous protrusion in an appliance surface or aridge. While the geometric features of ridge 12 may vary along thelength, the ridge is continuous in the sense that it is configured tocontact a tooth surface along an uninterrupted length. Ridge 12 isillustrated as having a more horizontal orientation relative to thetooth or, in other words, perpendicular to the tooth in the crown toroot direction. Referring to FIG. 1C, a continuous ridge 14 isillustrated disposed in an appliance cavity in a vertical orientation.FIG. 1D illustrates a non-continuous ridge 15 that is disposed in anappliance surface and vertically oriented. FIG. 1E shows across-sectional view of ridge 15, illustrating the sort of corrugatedsurface forming the non-continuous ridge by a series of dimples orbump-like protrusions 16 a, 16 b, 16 c. As illustrated, such bump-likeprotrusions can each include a portion of the protrusion that contacts atooth surface, with each tooth contacting surface of a protrusionseparated by non-tooth contacting regions of the ridge having adifferent height. Parameters of tooth contacting and non-contactingaspects of a non-continuous ridge, as illustrated, can be defined, asleast in part, by fabrication methods (e.g., direct fabrication, vacuummolding, etc.) used. Both continuous and non-continuous type ridgesfunction to apply a force vector along a length of the tooth, ratherthan at a single point as with a single dimple or bump-like protrusion.Shaped features, such as ridges can be designed in various shapes (e.g.,curve, “L” shaped, “T” shaped, hook, etc.), as well as orientations(e.g., vertical, horizontal, slanted, etc.) and are not limited to anyparticular shape or orientation.

Any number of one or more shaped features can be included in design andfabrication of an improved appliance of the present invention. In oneembodiment, a cavity of an appliance can include a plurality of shapedfeatures, such as protrusions. For example, a cavity can include atleast two shaped features such as protrusions that are shaped andpositioned within the cavity such that each of the protrusions arebrought into contact with the received patient's tooth when theappliance is initially worn by the patient. Thus, a number ofprotrusions (e.g., two or more) can configured and incorporated inappliance such that each of those protrusions will each engage thereceived tooth when the appliance is initially worn by the patient andbefore the tooth has been moved by the appliance.

Besides protrusions or non-attachment type shaped features, the shapedfeatures of the present invention can optionally include attachment typefeatures. Attachment, as used herein, may be any form of material thatmay be attached to the tooth whether preformed, formed using a templateor in an amorphous form that is attached to the surface of the tooth. Itcan be disposed on the tooth surface using an adhesive material, or theadhesive material itself may be disposed on the surface of the tooth asan attachment.

Generally, the attachments operate to provide “bumps” on a surface ofthe tooth which otherwise would be difficult for the dental appliance togrip. Attachments may also be engaged by the appliance in a manner thatfavors delivery of desired force directions and magnitudes. Attachmentstypically include a material bonded or attached to a surface of thetooth, with a corresponding receiving portion or couple built into thetooth receiving appliance. In one example, an attachment-type featurecan include an orphan attachment, or any appropriate shaped materialbonded to crown surface, but with no receptacle or receiving portionbuilt into the appliance to receive the attachment shape. Instead, thegenerated force concentrates on contact area between appliance surfaceand attachment.

Various tooth movements can be accomplished according to the presentinvention. Examples of specific movements that can be included and whichare further described below include translation, such as buccal-labiallingual translation, mesio-distal translation, extrusion, intrusion,root movements, first order rotation, second order root movement, andthird order root movement. However, the methods can be applied toachieve any type of tooth movement, in any direction, in any arbitraryplane of space.

Non-attachment type shaped features or protrusions can be included inthe present invention, and may optionally be utilized in conjunctionwith use of attachment type features as described above. In someinstances, such protrusions can be described in an analogous manner todescription in regard to attachments, for example, in terms positioningand application of selected forces to a tooth. In certain aspects,however, use of protrusion features (e.g., ridge-like protrusions) canprovide numerous differences and/or advantages compared to use ofattachments.

In still another aspect, the aligner features may be designed andfabricated to limit movement of the tooth. For example, the aligner maybe designed to be a physical boundary through which the tooth cannotmove providing safety against unwanted movements that may be deleteriousto the patient's health. Further, the aligner in another aspect may beconfigured to function as a guiding surface along which the tooth moves.More particularly, the aligner may be configured to impart a forcesystem to the tooth and the tooth may be guided into a specific locationand orientation assisted by the guidance of the aligner.

As set forth above, incorporation of one or more protrusions inappliance design according to the present invention can be utilized forvarious tooth movements. Non-limiting examples of specific movementsthat can be accomplished and which are further described below includetranslation, such as buccal-labial lingual translation, mesio-distaltranslation, extrusion, intrusion, first order rotation, second orderroot movement, and third order root movement. Exemplary tooth movementsand corresponding positioning of shaped features are described belowwith reference to corresponding figures (see, e.g., FIGS. 2A-2F, 3A-3D,4A-4C, and 5A-5B).

Buccal-Lingual Translation

Shaped features, including protrusions or ridge shaped features can beused for tooth translation, such as buccal or lingual translation. FIGS.2A-2F illustrate an appliance positioned on a tooth receiving cavity ofthe appliance including shaped feature(s) positioning for lingualtranslation. Illustrated shaped features include appliance protrusions,orphan attachments, or a combination thereof. As illustrated, to achievelingual translation, features on the buccal side are closer the gingivalline than the features on the lingual side. Stated another way,attachment to center of resistance (CR) length is greater on the lingualside compared to the buccal side. FIG. 2A shows interior ridge featuresare added to an appliance, including an interior ridge 18 a on thebuccal side and positioned closer to the gingival line (or to the centerof resistance), and an interior ridge 18 b on the lingual side andpositioned more distally compared to the buccal side ridge 18 a. Theparameters of the features will be selected and designed such that thelingual force generated from buccal features will be greater than thebuccal force from the lingual features. However, the directions of thesetwo force components are opposite. The lingual force has longer arm tothe center of resistance than the buccal force does. By adjusting thepositions and parameters of the buccal and lingual features, the tippingmoment from buccal features can be cancelled out by the counterbalancing moment from lingual features and the resultant is the lingualtranslation. FIG. 2B and FIG. 2C illustrate a similar concept, but withuse of shaped features in the forms of exterior ridges 20 a, 20 b (FIG.2B) and orphan attachments 22 a, 22 b (FIG. 2C) used for lingualtranslation.

In certain embodiments, a tooth receiving cavity may include only asingle protrusion or ridge-shaped feature. FIGS. 2D through 2Eillustrate use of a single protrusion for lingual translation. If thereis no feature added to the buccal side of aligner, the buccal surface ofaligner will generate a translation force toward lingual direction. Inanother embodiment, a feature can be added to lingual side alone tocreate a counter balance torque to the force generated from an appliancesurface in contact with the tooth on the opposing buccal side. FIG. 2Dillustrates a single protrusion feature 24 positioned on the buccal sideto impart a lingual force and illicit a counter balance torque from thecontact between the tooth and appliance. FIG. 2E shows a singleprotrusion feature 26 in the form of interior ridge on lingual side onlyof appliance cavity.

In another embodiment, a single protrusion can be used in conjunctionwith an attachment-type feature for the desired tooth movement. FIG. 2Fshows a buccal side orphan attachment 28 used with interior ridge 30 onlingual side of the appliance cavity. The various different shapes andtypes of features and protrusions can be utilized and/or combined toaccomplish lingual translation as described above.

Protrusion and shaped feature use can by selected for buccal translationand feature positioning can be selected in a manner analogous to theabove description regarding lingual translation (e.g., FIGS. 2A-2F). Incontrast to lingual translation, use of features for buccal translationwill include positioning of a lingual side feature or component closerto the gingival line relative to buccal side feature/componentplacement.

Mesial-Distal Translation

In another aspect, shaped features are used to accomplish mesial ordistal translation. As seen in FIG. 3A, where the desired movementincludes mesial translation, features (e.g., ridges) such as Feature 32a on the distal interproximal area will be positioned closer to thegingival line compared to features on the mesial interproximal area suchas Feature 32 b, while features on the mesial interproximal area will becloser to the occlusal plane. By controlling the parameters andpositions of features, the selected forces can include a mesial forceexceeding the distal force and the second order moment can be zeroedout. Spacing or room around the interproximal area can be created in thepatient's dentition to accommodate the features of the appliance. Insome embodiments, a single feature only may be included or featurespositioned only on a distal area or mesial area. FIG. 3C show theFeatures 36 positioned only on mesial surface for distal translation.FIG. 3D illustrates Features 38 positioned only on the distal surfacefor mesial translation.

Distal translation can be accomplished in a manner analogous to theabove description regarding mesial translation, but with features on themesial interproximal area positioned closer to the gingival linecompared to features on the distal interproximal area, with features onthe distal interproximal area positioned closer to the occlusal plane.FIG. 3B illustrates Features 34 a, 34 b positioning selected for distaltranslation.

Extrusion and Intrusion

In another aspect, feature design and positioning can be selected forextrusion and intrusion movements, as illustrated in FIGS. 4A-4C. Forextrusion, for example, features on appliance cavity can be positionedtoward the gingival line, as the buccal and lingual surfaces in thegingival half of the crown are usually undercut, as shown in FIGS. 4A(Features 40 a, 40 b) and 4C (Features 44 a, 44 b, 44 c, 44 d). Byselecting the parameters and positions of the features, the undercuttingcontact areas can provide total contact force extrusive, because theforces from each feature will be normal to the undercutting contactarea.

For intrusion, the features on aligner can be selected and positionedcloser toward the occlusal plane as the buccal and lingual surfaces inthe occlusal half of the crown are usually convex, as shown in FIGS. 4B(Features 42 a, 42 b) and 4C (Features 44 a, 44 b, 44 c, 44 d). Bytuning the parameters and positions of the features, the convex contactareas can provide total contact force intrusive, as the forces from eachfeature will be normal to the contact area.

Third Order Root Movement

In another aspect, as will be recognized, use of features as describedherein can be directed to various root movements. When a third orderroot movement (e.g., lingual root torque) is desired on tooth crown, thecrown will rotate buccally much less than the root will rotatelingually. The features on the buccal side can be positioned closer togingival line and the ones on lingual side are closer to occlusal plane(e.g., as shown in FIG. 2A). In such an instance, the features on thebuccal side will generate lingual force and the lingual features willgenerate buccal force. By configuring the parameters and positions offeatures, feature positioning can be selected such that the lingualforce exceeds buccal force. However, the directions of these two forcesare opposite, with the lingual force having a longer arm to the centerof resistance than the buccal force. By adjusting the positions andparameters of the buccal and lingual features, featuredesign/positioning can be selected such that the lingual featuresgenerate torquing moment greater than the buccal features, whichcombined with lingual total force results in lingual root torque. Asillustrated in FIG. 2D, buccal surface only features may be selected,without features on lingual surface of appliance cavity. A similarmechanism as described above applies, now that the lingual surface ofplain (e.g., no feature) appliance cavity surface works in place oflingual features. Buccal root torque can be figured out in an analogousmanner.

Second Order Root Movement

In another aspect, second order root movements can be accomplished. Inone embodiment, for a second order mesial root movement, cavity designcan be selected such that features on the distal interproximal area willbe closer to the gingival line, while features on the mesialinterproximal area will be closer to the occlusal plane (e.g., FIG. 3A).By controlling the parameters and positions of features, the mesialforce prevails. However, the directions of these two forces from the twoillustrated features are opposite, with the distal force having a longerarm to the center of resistance than the mesial force. By adjusting thepositions and parameters of the mesial and distal features, the mesialfeatures generate second order moment greater than the force generatedby the distal features, which combined with mesial total force resultsin a second order root movement.

As above, features may be present only on one side of the appliancecavity. For example, FIG. 3D shows features only on a distal surface forsecond order mesial root movement. The same mechanism still applies asdescribed above, now that the mesial surface of plain aligner works inplace of mesial features.

Second order distal root movement can be figured out in an analogousmanner as described with regard to second order mesial root movement,but with features on the distal interproximal area positioned closer tothe occlusal plan (see, e.g., FIG. 4B).

First Order Rotation

In another aspect, first order rotations can be selected. In oneembodiment of a first order rotation, the parameters and positions offeatures will be configured to provide a couple about the occlusalgingival direction, as shown in FIGS. 5A (e.g., Features 46 a, 46 b) and5B (e.g., Features 48 a, 48 b). A couple is a moment generated by a pairof forces oriented parallel to one another, equal in magnitude andopposite in sense. The resultant force is zero.

As described above, a patient's teeth are generally progressivelyrepositioned according to a treatment plan. Exemplary methods treatmentplan design, as well as appliance design and fabrication are describedfurther below. Typically, appliance and/or treatment plan canoptionally, though not necessarily, be accomplished using variouscomputer based applications. It will be recognized that appliance designand fabrication is not limited to any particular method and can includevarious computer and non-computer based methodologies.

Treatment planning, according to one embodiment of the presentinvention, is described. Patient data can be collected and analyzed, andspecific treatment steps specified and/or prescribed. In one embodiment,a treatment plan can be generated and proposed for a dental practitionerto review. The dental practitioner can accept or request modificationsto the treatment plan. Once the treatment plan is approved,manufacturing of appliance(s) can begin. Digital treatment plans are nowpossible with 3-dimensional orthodontic treatment planning tools such assoftware from Align Technology, Inc. or other software available fromeModels and OrthoCAD, among others. These technologies allow theclinician to use the actual patient's dentition as a starting point forcustomizing the treatment plan. The software technology available fromAlign Technology, Inc., uses a patient-specific digital model to plot atreatment plan, and then use a scan of the achieved or actual treatmentoutcome to assess the degree of success of the outcome as compared tothe original digital treatment plan as discussed in U.S. patentapplication Ser. No. 10/640,439, filed Aug. 21, 2003 and U.S. patentapplication Ser. No. 10/225,889 filed Aug. 22, 2002. The problem withthe digital treatment plan and outcome assessment is the abundance ofdata and the lack of standards and efficient methodology by which toassess “treatment success” at an individual patient level. To analyzethe information, a dental data mining system is used.

FIG. 6A illustrates the general flow of an exemplary process 100 forgenerating a treatment plan or defining and generating repositioningappliances for orthodontic treatment of a patient. The process 100includes the methods, and is suitable for the apparatus, of the presentinvention, as will be described. The computational steps of the processare advantageously implemented as computer program modules for executionon one or more conventional digital computers.

As an initial step, a mold or a scan of patient's teeth or mouth tissueis acquired (110). This step generally involves taking casts of thepatient's teeth and gums, and may in addition or alternately involvetaking wax bites, direct contact scanning, x-ray imaging, tomographicimaging, sonographic imaging, and other techniques for obtaininginformation about the position and structure of the teeth, jaws, gumsand other orthodontically relevant tissue. From the data so obtained, adigital data set is derived that represents the initial (that is,pretreatment) arrangement of the patient's teeth and other tissues.

The initial digital data set, which may include both raw data fromscanning operations and data representing surface models derived fromthe raw data, is processed to segment the tissue constituents from eachother (step 120). In particular, in this step, data structures thatdigitally represent individual tooth crowns are produced.Advantageously, digital models of entire teeth are produced, includingmeasured or extrapolated hidden surfaces and root structures as well assurrounding bone and soft tissue.

The desired final position of the teeth—that is, the desired andintended end result of orthodontic treatment—can be received from aclinician in the form of a prescription, can be calculated from basicorthodontic principles, or can be extrapolated computationally from aclinical prescription (step 130). With a specification of the desiredfinal positions of the teeth and a digital representation of the teeththemselves, the final position and surface geometry of each tooth can bespecified (step 140) to form a complete model of the teeth at thedesired end of treatment. Generally, in this step, the position of everytooth is specified. The result of this step is a set of digital datastructures that represents an orthodontically correct repositioning ofthe modeled teeth relative to presumed-stable tissue. The teeth andtissue are both represented as digital data.

Having both a beginning position and a final position for each tooth,the process next defines a tooth path for the motion of each tooth. Inone embodiment, the tooth paths are optimized in the aggregate so thatthe teeth are moved in the quickest fashion with the least amount ofround-tripping to bring the teeth from their initial positions to theirdesired final positions. (Round-tripping is any motion of a tooth in anydirection other than directly toward the desired final position.Round-tripping is sometimes necessary to allow teeth to move past eachother.) The tooth paths are segmented. The segments are calculated sothat each tooth's motion within a segment stays within threshold limitsof linear and rotational translation. In this way, the end points ofeach path segment can constitute a clinically viable repositioning, andthe aggregate of segment end points constitute a clinically viablesequence of tooth positions, so that moving from one point to the nextin the sequence does not result in a collision of teeth.

The threshold limits of linear and rotational translation areinitialized, in one implementation, with default values based on thenature of the appliance to be used. More individually tailored limitvalues can be calculated using patient-specific data. The limit valuescan also be updated based on the result of an appliance-calculation(step 170, described later), which may determine that at one or morepoints along one or more tooth paths, the forces that can be generatedby the appliance on the then-existing configuration of teeth and tissueis incapable of effecting the repositioning that is represented by oneor more tooth path segments. With this information, the subprocessdefining segmented paths (step 150) can recalculate the paths or theaffected subpaths.

At various stages of the process, and in particular after the segmentedpaths have been defined, the process can, and generally will, interactwith a clinician responsible for the treatment of the patient (step160). Clinician interaction can be implemented using a client processprogrammed to receive tooth positions and models, as well as pathinformation from a server computer or process in which other steps ofprocess 100 are implemented. The client process is advantageouslyprogrammed to allow the clinician to display an animation of thepositions and paths and to allow the clinician to reset the finalpositions of one or more of the teeth and to specify constraints to beapplied to the segmented paths. If the clinician makes any such changes,the subprocess of defining segmented paths (step 150) is performedagain.

The segmented tooth paths and associated tooth position data are used tocalculate clinically acceptable appliance configurations (or successivechanges in appliance configuration) that will move the teeth on thedefined treatment path in the steps specified by the path segments (step170). Each appliance configuration represents a step along the treatmentpath for the patient. The steps are defined and calculated so that eachdiscrete position can follow by straight-line tooth movement or simplerotation from the tooth positions achieved by the preceding discretestep and so that the amount of repositioning required at each stepinvolves an orthodontically optimal amount of force on the patient'sdentition. As with the path definition step, this appliance calculationstep can include interactions and even iterative interactions with theclinician (step 160). The operation of a process step 200 implementingthis step will be described more fully below.

Having calculated appliance definitions, the process 100 can proceed tothe manufacturing step (step 180) in which appliances defined by theprocess are manufactured, or electronic or printed information isproduced that can be used by a manual or automated process to defineappliance configurations or changes to appliance configurations.

FIG. 6B illustrates a process 200 implementing the appliance-calculationstep (FIG. 6A, step 170) for polymeric shell aligners of the kinddescribed in above-mentioned U.S. Pat. No. 5,975,893. Inputs to theprocess include an initial aligner shape 202, various control parameters204, and a desired end configuration for the teeth at the end of thecurrent treatment path segment 206. Other inputs include digital modelsof the teeth in position in the jaw, models of the jaw tissue, andspecifications of an initial aligner shape and of the aligner material.Using the input data, the process creates a finite element model of thealigner, teeth and tissue, with the aligner in place on the teeth (step210). Next, the process applies a finite element analysis to thecomposite finite element model of aligner, teeth and tissue (step 220).The analysis runs until an exit condition is reached, at which time theprocess evaluates whether the teeth have reached the desired endposition for the current path segment, or a position sufficiently closeto the desired end position (step 230). If an acceptable end position isnot reached by the teeth, the process calculates a new candidate alignershape (step 240). If an acceptable end position is reached, the motionsof the teeth calculated by the finite elements analysis are evaluated todetermine whether they are orthodontically acceptable (step 232). Ifthey are not, the process also proceeds to calculate a new candidatealigner shape (step 240). If the motions are orthodontically acceptableand the teeth have reached an acceptable position, the current alignershape is compared to the previously calculated aligner shapes. If thecurrent shape is the best solution so far (decision step 250), it issaved as the best candidate so far (step 260). If not, it is saved in anoptional step as a possible intermediate result (step 252). If thecurrent aligner shape is the best candidate so far, the processdetermines whether it is good enough to be accepted (decision step 270).If it is, the process exits. Otherwise, the process continues andcalculates another candidate shape (step 240) for analysis.

The finite element models can be created using computer programapplication software available from a variety of vendors. For creatingsolid geometry models, computer aided engineering (CAE) or computeraided design (CAD) programs can be used, such as the AutoCAD® softwareproducts available from Autodesk, Inc., of San Rafael, Calif. Forcreating finite element models and analyzing them, program products froma number of vendors can be used, including the PolyFEM product availablefrom CADSI of Coralville, Iowa, the Pro/Mechanica simulation softwareavailable from Parametric Technology Corporation of Waltham, Mass., theI-DEAS design software products available from Structural DynamicsResearch Corporation (SDRC) of Cincinnati, Ohio, and the MSC/NASTRANproduct available from MacNeal-Schwendler Corporation of Los Angeles,Calif.

FIG. 7 shows a process 300 of creating a finite element model that canbe used to perform step 210 of the process 200 (FIG. 6B). Input to themodel creation process 300 includes input data 302 describing the teethand tissues and input data 304 describing the aligner. The input datadescribing the teeth 302 include the digital models of the teeth;digital models of rigid tissue structures, if available; shape andviscosity specifications for a highly viscous fluid modeling thesubstrate tissue in which the teeth are embedded and to which the teethare connected, in the absence of specific models of those tissues; andboundary conditions specifying the immovable boundaries of the modelelements. In one implementation, the model elements include only modelsof the teeth, a model of a highly viscous embedding substrate fluid, andboundary conditions that define, in effect, a rigid container in whichthe modeled fluid is held. Note that fluid characteristics may differ bypatient clusters, for example as a function of age.

A finite element model of the initial configuration of the teeth andtissue is created (step 310) and optionally cached for reuse in lateriterations of the process (step 320). As was done with the teeth andtissue, a finite element model is created of the polymeric shell aligner(step 330). The input data for this model includes data specifying thematerial of which the aligner is made and the shape of the aligner (datainput 304).

The model aligner is then computationally manipulated to place it overthe modeled teeth in the model jaw to create a composite model of anin-place aligner (step 340). Optionally, the forces required to deformthe aligner to fit over the teeth, including any hardware attached tothe teeth, are computed and used as a figure of merit in measuring theacceptability of the particular aligner configuration. Optionally, thetooth positions used are as estimated from a probabilistic model basedon prior treatment steps and other patient information. In a simpleralternative, however, the aligner deformation is modeled by applyingenough force to its insides to make it large enough to fit over theteeth, placing the model aligner over the model teeth in the compositemodel, setting the conditions of the model teeth and tissue to beinfinitely rigid, and allowing the model aligner to relax into positionover the fixed teeth. The surfaces of the aligner and the teeth aremodeled to interact without friction at this stage, so that the alignermodel achieves the correct initial configuration over the model teethbefore finite element analysis is begun to find a solution to thecomposite model and compute the movement of the teeth under theinfluence of the distorted aligner.

FIG. 8 shows a process 400 for calculating the shape of a next alignerthat can be used in the aligner calculations, step 240 of process 200(FIG. 6B). A variety of inputs are used to calculate the next candidatealigner shape. These include inputs 402 of data generated by the finiteelement analysis solution of the composite model and data 404 defined bythe current tooth path. The data 402 derived from the finite elementanalysis includes the amount of real elapsed time over which thesimulated repositioning of the teeth took place; the actual end toothpositions calculated by the analysis; the maximum linear and torsionalforce applied to each tooth; the maximum linear and angular velocity ofeach tooth. From the input path information, the input data 404 includesthe initial tooth positions for the current path segment, the desiredtooth positions at the end of the current path segment, the maximumallowable displacement velocity for each tooth, and the maximumallowable force of each kind for each tooth.

If a previously evaluated aligner was found to violate one or moreconstraints, additional input data 406 can optionally be used by theprocess 400. This data 406 can include information identifying theconstraints violated by, and any identified suboptimal performance of,the previously evaluated aligner. Additionally, input data 408 relatingto constraints violated by, and suboptimal performance of previousdental devices can be used by the process 400.

Having received the initial input data (step 420), the process iteratesover the movable teeth in the model. (Some of the teeth may beidentified as, and constrained to be, immobile.) If the end position anddynamics of motion of the currently selected tooth by the previouslyselected aligner is acceptable (“yes” branch of decision step 440), theprocess continues by selecting for consideration a next tooth (step 430)until all teeth have been considered (“done” branch from step 430 tostep 470). Otherwise (“no” branch from step 440), a change in thealigner is calculated in the region of the currently selected tooth(step 450). The process then moves back to select the next current tooth(step 430) as has been described.

When all of the teeth have been considered, the aggregate changes madeto the aligner are evaluated against previously defined constraints(step 470), examples of which have already been mentioned. Constraintscan be defined with reference to a variety of further considerations,such as manufacturability. For example, constraints can be defined toset a maximum or minimum thickness of the aligner material, or to set amaximum or minimum coverage of the aligner over the crowns of the teeth.If the aligner constraints are satisfied, the changes are applied todefine a new aligner shape (step 490). Otherwise, the changes to thealigner are revised to satisfy the constraints (step 480), and therevised changes are applied to define the new aligner shape (step 490).

FIG. 9A illustrates one implementation of the step of computing analigner change in a region of a current tooth (step 450). In thisimplementation, a rule-based inference engine 456 is used to process theinput data previously described (input 454) and a set of rules 452 a-452n in a rule base of rules 452. The inference engine 456 and the rules452 define a production system which, when applied to the factual inputdata, produces a set of output conclusions that specify the changes tobe made to the aligner in the region of the current tooth (output 458).

Rules 452 a . . . 452 n have the conventional two-part form: an if-partdefining a condition and a then-part defining a conclusion or actionthat is asserted if the condition is satisfied. Conditions can be simpleor they can be complex conjunctions or disjunctions of multipleassertions. An exemplary set of rules, which defines changes to be madeto the aligner, includes the following: if the motion of the tooth istoo fast, add driving material to the aligner opposite the desireddirection of motion; if the motion of the tooth is too slow, add drivingmaterial to overcorrect the position of the tooth; if the tooth is toofar short of the desired end position, add material to overcorrect; ifthe tooth has been moved too far past the desired end position, addmaterial to stiffen the aligner where the tooth moves to meet it; if amaximum amount of driving material has been added, add material toovercorrect the repositioning of the tooth and do not add drivingmaterial; if the motion of the tooth is in a direction other than thedesired direction, remove and add material so as to redirect the tooth.

In an alternative embodiment, illustrated in FIGS. 9B and 9C, anabsolute configuration of the aligner is computed, rather than anincremental difference. As shown in FIG. 9B, a process 460 computes anabsolute configuration for an aligner in a region of a current tooth.Using input data that has already been described, the process computesthe difference between the desired end position and the achieved endposition of the current tooth (462). Using the intersection of the toothcenter line with the level of the gum tissue as the point of reference,the process computes the complement of the difference in all six degreesof freedom of motion, namely three degrees of translation and threedegrees of rotation (step 464). Next, the model tooth is displaced fromits desired end position by the amounts of the complement differences(step 466), which is illustrated in FIG. 9B.

FIG. 9D shows a planar view of an illustrative model aligner 60 over anillustrative model tooth 62. The tooth is in its desired end positionand the aligner shape is defined by the tooth in this end position. Theactual motion of the tooth calculated by the finite element analysis isillustrated as placing the tooth in position 64 rather than in thedesired position 62. A complement of the computed end position isillustrated as position 66. The next step of process 460 (FIG. 9B)defines the aligner in the region of the current tooth in this iterationof the process by the position of the displaced model tooth (step 468)calculated in the preceding step (466). This computed alignerconfiguration in the region of the current tooth is illustrated in FIG.9D as shape 68 which is defined by the repositioned model tooth inposition 66.

A further step in process 460, which can also be implemented as a rule452 (FIG. 9A), is shown in FIG. 9C. To move the current tooth in thedirection of its central axis, the size of the model tooth defining thatregion of the aligner, or the amount of room allowed in the aligner forthe tooth, is made smaller in the area away from which the process hasdecided to move the tooth (step 465).

As shown in FIG. 10, the process 200 (FIG. 6B) of computing the shapefor an aligner for a step in a treatment path is one step in a process600 of computing the shapes of a series of aligners. This process 600begins with an initialization step 602 in which initial data, controland constraint values are obtained.

When an aligner configuration has been found for each step or segment ofthe treatment path (step 604), the process 600 determines whether all ofthe aligners are acceptable (step 606). If they are, the process iscomplete. Otherwise, the process optionally undertakes a set of steps610 in an attempt to calculate a set of acceptable aligners. First, oneor more of the constraints on the aligners is relaxed (step 612). Then,for each path segment with an unacceptable aligner, the process 200(FIG. 6B) of shaping an aligner is performed with the new constraints(step 614). If all the aligners are now acceptable, the process 600exits (step 616).

Aligners may be unacceptable for a variety of reasons, some of which arehandled by the process. For example, if any impossible movements wererequired (decision step 620), that is, if the shape calculation process200 (FIG. 6B) was required to effect a motion for which no rule oradjustment was available, the process 600 proceeds to execute a modulethat calculates the configuration of a hardware attachment to thesubject tooth to which forces can be applied to effect the requiredmotion (step 640). Because adding hardware can have an effect that ismore than local, when hardware is added to the model, the outer loop ofthe process 600 is executed again (step 642).

If no impossible movements were required (“no” branch from step 620),the process transfers control to a path definition process (such as step150, FIG. 6A) to redefine those parts of the treatment path havingunacceptable aligners (step 630). This step can include both changingthe increments of tooth motion, i.e., changing the segmentation, on thetreatment path, changing the path followed by one or more teeth in thetreatment path, or both. After the treatment path has been redefined,the outer loop of the process is executed again (step 632). Therecalculation is advantageously limited to recalculating only thosealigners on the redefined portions of the treatment path. If all thealigners are now acceptable, the process exits (step 634). Ifunacceptable aligners still remain, the process can be repeated until anacceptable set of aligners is found or an iteration limit is exceeded(step 650). At this point, as well as at other points in the processesthat are described in this specification, such as at the computation ofadditional hardware (step 640), the process can interact with a humanoperator, such as a clinician or technician, to request assistance (step652). Assistance that an operator provides can include defining orselecting suitable attachments to be attached to a tooth or a bone,defining an added elastic element to provide a needed force for one ormore segments of the treatment path, suggesting an alteration to thetreatment path, either in the motion path of a tooth or in thesegmentation of the treatment path, and approving a deviation from orrelaxation of an operative constraint.

As was mentioned above, the process 600 is defined and parameterized byvarious items of input data (step 602). In one implementation, thisinitializing and defining data includes the following items: aniteration limit for the outer loop of the overall process; specificationof figures of merit that are calculated to determine whether an aligneris good enough (see FIG. 6B, step 270); a specification of the alignermaterial; a specification of the constraints that the shape orconfiguration of an aligner must satisfy to be acceptable; aspecification of the forces and positioning motions and velocities thatare orthodontically acceptable; an initial treatment path, whichincludes the motion path for each tooth and a segmentation of thetreatment path into segments, each segment to be accomplished by onealigner; a specification of the shapes and positions of any anchorsinstalled on the teeth or otherwise; and a specification of a model forthe jaw bone and other tissues in or on which the teeth are situated (inthe implementation being described, this model consists of a model of aviscous substrate fluid in which the teeth are embedded and which hasboundary conditions that essentially define a container for the fluid).

Various tooth root imaging and/or modeling (e.g., statistical rootmodeling) may be utilized. The teeth movement can be guided in partusing a root-based sequencing system. In one embodiment, the movement isconstrained by a surface area constraint, while in another embodiment,the movement is constrained by a volume constraint.

Optionally, other features are added to the tooth model data sets toproduce desired features in the aligners. For example, it may bedesirable to add digital wax patches to define cavities or recesses tomaintain a space between the aligner and particular regions of the teethor jaw. It may also be desirable to add digital wax patches to definecorrugated or other structural forms to create regions having particularstiffness or other structural properties. In manufacturing processesthat rely on generation of positive models to produce the repositioningappliance, adding a wax patch to the digital model will generate apositive mold that has the same added wax patch geometry. This can bedone globally in defining the base shape of the aligners or in thecalculation of particular aligner shapes. One feature that can be addedis a rim around the gumline, which can be produced by adding a digitalmodel wire at the gumline of the digital model teeth from which thealigner is manufactured. When an aligner is manufactured by pressurefitting polymeric material over a positive physical model of the digitalteeth, the wire along the gumlines causes the aligner to have a rimaround it providing additional stiffness along the gumline.

In another optional manufacturing technique, two or more sheets ofmaterial are pressure fit over the positive tooth model, where one ofthe sheets is cut along the apex arch of the aligner and the other(s) isoverlaid on top. This provides at least a double thickness of alignermaterial along the vertical walls of the teeth.

The changes that can be made to the design of an aligner are constrainedby the manufacturing technique that will be used to produce it. Forexample, if the aligner will be made by pressure fitting a polymericsheet over a positive model, the thickness of the aligner is determinedby the thickness of the sheet. As a consequence, the system willgenerally adjust the performance of the aligner by changing theorientation of the model teeth, the sizes of parts of the model teeth,the position and selection of attachments, and the addition or removalof material (e.g., adding virtual wires or creating protrusions (e.g.,ridges, dimples, etc.), creating modification (e.g., modifications tocompensate for protrusion mediated distortions)) to change the structureof the aligner. The system can optionally adjust the aligner byspecifying that one or more of the aligners are to be made of a sheet ofa thickness other than the standard one, to provide more or less forceto the teeth. On the other hand, if the aligner will be made by a stereolithography process, the thickness of the aligner can be varied locally,and structural features such as rims, dimples, and corrugations can beadded without modifying the digital model of the teeth.

The system can also be used to model the effects of more traditionalappliances such as retainers and braces and therefore be used togenerate optimal designs and treatment programs for particular patients.

Thus, one or more shaped features or protrusions can be selectivelyadded and included in appliance design and fabrication, with appliancedesign and fabrication, and incorporation of appliances in a treatmentplan as described above. In some instances, however, incorporation of ashaped feature or protrusion into an appliance may result in asubsequent change in the geometry of the appliance at other surfaces ofthe appliance, e.g., when worn by the patient. Such changes oralterations can result in changes in property or location of contactsurfaces between the tooth and the appliance, sometimes in anundesirable manner. As such, changes or distortions can be modeled oraccounted for in appliance design. For example, changes, distortions andthe like can be analyzed or determined computationally in terms ofprobability of occurrence, as well as whether such changes/distortionswould be beneficial or detrimental to the desired loading and toothmovement. Methods can be included to determine the effect of thesegeometric changes and compensate for them by identifying new surfaces orshapes, and loadings to accomplish the desired movement. Appliancegeometry can therefore be improved in this iterative design process, asthe process in turn considers each feature and its effect on theappliance geometry, on surfaces of contact, and on the force systemproduced in the designing of an appliance.

Modification of an appliance surface to compensate for an effect (e.g.,distortion effect) due to incorporation of a protrusion, according to anembodiment of the present invention, is illustrated with reference toFIGS. 11A-11C, and FIG. 12. FIGS. 11A-11B illustrate an initial toothposition with a positioned dental appliance, and a resulting undesirableforce vector, respectively. Referring to the Figures, in an examplewhere the tooth as shown is being moved in a facial direction along thex-direction, upon positioning of the dental appliance such as thepolymeric shell aligner, over the tooth, the aligner shape geometry isconfigured to apply a predetermined force upon the tooth to repositionthe tooth in accordance with a treatment plan for the particulartreatment stage. For example, as shown in FIG. 11B, the dental applianceis configured to fit over the tooth to reposition the tooth in thex-direction as shown, but, rather, results in the application of apredetermined force in the +x/−z direction as shown and illustrated bythe arrow. Appliances can include one or more shaped features disposedin a cavity.

Accordingly, in one aspect, the aligner shape geometry may be optimizedto compensate for the undesirable but resulting force vector so as tocounteract its force and further, to apply the intended force in thedirection based on the treatment plan for the treatment stage underconsideration. One exemplary modification can include addition of arelief component. FIGS. 11C-11D illustrate a relief addition to thedental appliance to counteract the undesirable force vector around thetooth, and the resulting desired application of the predetermined forceon the tooth by the dental appliance, respectively. In one aspect, tocompensate for the undesirable force (for example, as shown in FIG. 11Bby the arrow), a predetermined relief (for example, but not limited to,0.1 to 0.3 mm) may be provided such that the contact between the alignerand the tooth that resulted in the undesirable force vector is avoided,but still retaining the desired force, for example, along the x-axis asdiscussed above.

Referring to FIGS. 11C, the predetermined relief on the aligner isillustrated by the shown arrow, whereby the engagement between thealigner and the tooth at the location resulting in the undesirable forceis removed by modifying the shape of the aligner geometry. In thismanner, in one aspect, and as shown in FIG. 11D, the intended anddesirable force applied upon the tooth for example, in the x-direction,is achieved by, for example, modifying the aligner shape geometry.

FIG. 12 illustrates a modified dental appliance geometry including anadditional shape modification to remove a gap between the dentalappliance and the tooth. Referring to FIG. 12, it is to be noted thatwhile the modification of the aligner shape geometry (for example,discussed above in conjunction with FIGS. 11C-11D), results in thedesired predetermined force applied upon the tooth as planned for thedental treatment, there may be a gap or pocket that forms between thetooth and the aligner, for example, as shown in FIG. 12, near thegingival area. In one aspect, to account for this gap or pocketgenerated, the aligner shape geometry may be further modified oroptimized, for example, to better adapt in the direction towards thetooth when the aligner is in the active (or stretched) state.

Referring to FIG. 12, the optimization of the aligner shape geometry toaddress the formed gap or pocket is illustrated by the arrow in oneembodiment, in the direction of which, the aligner shape may bemodified. Moreover, it should be noted that the optimization of thealigner shape to account for the gap may potentially effect thedirection of the applied force on the tooth by the aligner, and thus,may further require additional modification or optimization.

In one aspect, the modification of the dental aligner shape geometrywith one or more areas of modification (e.g., relief, etc.), as well asrecontouring for looser or tighter adaptation, respectively, to achievethe desired force vector, while avoiding friction and other undesirableforce vectors provides improved and customized aligner shape for thetreatment of the dental conditions.

In manufacturing of the dental appliances, in one aspect, thestereolithography mold may be adjusted during the build process to takeshape of the desired geometry based on, for example, digitally addingand/or subtracting the relief and/or protrusion in predefined orrelevant locations of the mold.

In one aspect, based on the force behavior determined from the materialproperties and the amount of surface area perpendicular to the compositevector resulting from the movement vector for the particular treatmentstage, additional surface area may be added to the tooth by employing ashaped feature specifically suited for the desired movement. In thismanner, in one aspect, the cross section and/or orientation of thesurface area may be determined for a particular tooth, and the shapedfeature(s) can be incorporated on one or more teeth to enhance orimprove upon the necessary surface area to cooperate or engage with thedental appliance to effect the desired movement vector or thepredetermined level of force upon the tooth in the accurate directionfor the treatment stage.

In this manner, in one aspect, a dental aligner may be manufactured orsimulated using a computer aided design tool or system, where, arepresentation of the tooth to be moved is first modeled. Thereafter,the aligner that defines the target position of the tooth is modeledwith shape geometry properties defined. Thereafter, the force necessaryto reposition the tooth from the initial location to the target locationis determined or modeled, for example, using FEA modeling, or othersuitable computation and/or modeling techniques. In one aspect, it ispossible to define the force using a physical model of the teethconnected to force measurement sensors, such that the optimal forces maybe determined using the readouts obtained from the physical model, andthus altering the shapes of features (e.g., ridge protrusions, dimpledprotrusions, etc.) and aligner configurations based at least in part onthe feedback from the physical force gauge.

As a result, a movement vector is defined which establishes thedirection of the applied force, as well as the level of force and itsproperties which are necessary to reposition the tooth from the initialposition to the target position. Based on the movement vector, and themodeled aligner shape, the aligner is further modified or reconfiguredto factor in the determined movement vector. That is, after havingdefined the movement vector which identifies the force propertiesnecessary for the tooth repositioning, the dental appliance shape isaltered or optimized based on the determined movement vector.Additionally, the appliance shape may be further optimized to counteractthe undesirable forces or force components, or appliance distortion(e.g., due to a protrusion) that may result based on the definedmovement vector.

Thereafter, the modified or optimized dental appliance may bemanufactured through stereolithography or other suitable techniques toattain the desired tooth movement. Further, this process may be repeatedfor the optimization of dental appliance for each treatment stage of thetreatment plan such that the aligner performance and therefore, thetreatment plan result is improved.

Furthermore, in yet still another aspect, shaped feature placement maybe determined based on the location of the maximum amount of surfacearea available perpendicular to the desired direction of the toothmovement. Further, if the force on any given tooth in the treatment planis at or below a predefined level, the feature (e.g., protrusion) may beadded to the tooth or appliance to supplement the desired surface areaor increase the friction coefficient of the tooth, thereby improving theforce profile of the aligner on the tooth.

In one aspect, the data set associated with the teeth, gingiva and/orother oral tissue or structures may be intentionally altered through,for example, addition, partial or total subtraction, uniform ornon-uniform scaling, Boolean or non-Boolean algorithm, or geometricoperations, or one or more combinations thereof, for the configuration,modeling and/or manufacturing of the dental appliance that may beoptimized for the desired or intended treatment goal.

Accordingly, in one aspect, the n+1 or subsequent/target tooth positionis first determined. Thereafter, the direction of movement to reach thetarget tooth position from the initial tooth position is determined.After determining the direction of movement, the amount or magnitude anddirection of force and torque to reposition the tooth from the initialposition to the target position is determined. Thereafter, profile ofthe appliance cavity and features/protrusions disposed therein, such asthe geometry that would provide the most suitable load vector in thedirection of the planned tooth movement is determined, as well as theoptimal position of the shaped feature relative to the tooth surface. Inthis manner, the force/torque generated by the dental appliance isaccurately directed in the desired direction, and also is configuredwith sufficient magnitude to move the tooth into the next plannedposition.

In one aspect, the direction and the magnitude of the force/torque maybe modified or optimized to generate counter-balancing force/torque toeliminate or minimize unwanted tipping torque, to attain root movement,and the like, by adjusting the profile and/or positioning of the shapedfeatures relative to the crown surface, for example. The amount of thefeature movement with respect to the tooth crown may also be correlatedwith the tooth movement to generate a treatment plan based on themovement of the features.

FIG. 13 is a flowchart illustrating the optimized shape geometry of thedental appliance. Referring to FIG. 13, at step 2110, the initialposition of the tooth is determined. Thereafter, at step 2120, thetarget position of the tooth based on the treatment plan is determined.In one aspect, the target position may include the next or n+1 treatmentstage tooth position. Referring back to FIG. 13, after determining thetarget position of the tooth based on the treatment plan, a movementvector associated with the tooth movement from the initial position tothe target position is calculated or determined at step 2130. That is, aforce profile or attributes is determined which includes, for example,the magnitude of the force and the direction of the force, for example,that is associated with the tooth movement from the initial position tothe target position.

Referring again to FIG. 13, after determining the movement vectorassociated with the tooth movement from the initial position to thetarget position, at step 2140, the components associated with themovement vector are determined. For example, as discussed above, theforce magnitude associated with the movement vector to reposition thetooth from the initial position to the target position is determined.Additionally, the force direction for the tooth movement, as well ascounter forces for addressing unwanted or unintended forces aredetermined. Thereafter, based on the determined components associatedwith the movement vector which is associated with the tooth movementfrom the initial position to the target position, the cavity geometry ofthe dental appliance such as the aligner is modified.

FIG. 22 is a flowchart illustrating the shaped feature(s) (e.g., ridges,dimples, etc.) profile determination and positioning. Referring to FIG.22, at step 2210 the tooth position at a first treatment stage isdetermined. At step 2220 the tooth position at the second or n+1treatment stage is determined. Thereafter, the movement vectorassociated with the tooth movement from the first treatment stage to thesecond treatment stage is determined at step 2230. After determining themovement vector associated with the tooth movement, one or more shapedfeature(s) profile associated with the movement vector is determined atstep 2240. Thereafter, at step 2250, the one or more shaped features arepositioned, e.g., in the appliance (tooth receiving cavity), for contactwith the corresponding tooth during the first treatment stage. Theshaped feature profile and positioning are selected to achieve thedesired tooth movement.

In this manner, in one embodiment, the force/torque from the dentalappliance is accurately applied to the tooth to reposition the toothfrom the initial position to the target or second treatment stageposition.

The present invention can make use of various computer implementedembodiments of the methods described herein. For example, a computerimplemented method in one embodiment includes establishing an initialposition of a tooth, determining a target position of the tooth in atreatment plan, calculating a movement vector associated with the toothmovement from the initial position to the target position, determining aplurality of components corresponding to the movement vector, anddetermining a corresponding one or more positions/profiles of arespective one or more shaped features. The shaped features may beconfigured to apply a predetermined force on the dental appliancesubstantially at the surface plane of the tooth.

An apparatus for modeling a dental appliance in another embodimentincludes a data storage unit, and a processing unit coupled to the datastorage unit and configured to determine an initial position of a tooth,determine a target position of the tooth in a treatment plan, calculatea movement vector associated with the tooth movement from the initialposition to the target position, determine a plurality of componentscorresponding to the movement vector, and determine a profile and/orpositioning of corresponding one or more shaped features.

The data processing aspects of the invention can be implemented indigital electronic circuitry, or in computer hardware, firmware,software, or in combinations of them. Data processing apparatus of theinvention can be implemented in a computer program product tangiblyembodied in a machine-readable storage device for execution by aprogrammable processor; and data processing method steps of theinvention can be performed by a programmable processor executing aprogram of instructions to perform functions of the invention byoperating on input data and generating output. The data processingaspects of the invention can be implemented advantageously in one ormore computer programs that are executable on a programmable systemincluding at least one programmable processor coupled to receive dataand instructions from and to transmit data and instructions to a datastorage system, at least one input device, and at least one outputdevice. Each computer program can be implemented in a high-levelprocedural or object oriented programming language, or in assembly ormachine language, if desired; and, in any case, the language can be acompiled or interpreted language. Suitable processors include, by way ofexample, both general and special purpose microprocessors. Generally, aprocessor will receive instructions and data from a read-only memoryand/or a random access memory. Storage devices suitable for tangiblyembodying computer program instructions and data include all forms ofnonvolatile memory, including by way of example semiconductor memorydevices, such as EPROM, EEPROM, and flash memory devices; magnetic diskssuch as internal hard disks and removable disks; magneto-optical disks;and CD-ROM disks. Any of the foregoing can be supplemented by, orincorporated in, ASICs (application-specific integrated circuits).

To provide for interaction with a user, the invention can be implementedusing a computer system having a display device such as a monitor or LCD(liquid crystal display) screen for displaying information to the userand input devices by which the user can provide input to the computersystem such as a keyboard, a two-dimensional pointing device such as amouse or a trackball, or a three-dimensional pointing device such as adata glove or a gyroscopic mouse. The computer system can be programmedto provide a graphical user interface through which computer programsinteract with users. The computer system can be programmed to provide avirtual reality, three-dimensional display interface.

Various other modifications and alterations in the structure and methodof operation of this invention will be apparent to those skilled in theart without departing from the scope and spirit of the invention.Although the invention has been described in connection with specificpreferred embodiments, it should be understood that the invention asclaimed should not be unduly limited to such specific embodiments. It isintended that the following claims define the scope of the presentinvention and that structures and methods within the scope of theseclaims and their equivalents be covered thereby.

1. An orthodontic appliance for repositioning a patient's teeth,comprising: a shell appliance having teeth receiving cavities, at leastone of the cavities shaped to apply a resiliently repositioning forcewhen the appliance is worn by the patient so as to move the patient'steeth from the current arrangement toward the target arrangement, theshell further comprising at least one a ridge-shaped protrusion disposedin a repositioning cavity and configured to apply a repositioning forceto a patient's tooth corresponding to a selected tooth movement.
 2. Theappliance of claim 1, wherein the at least one cavity comprises only asingle protrusion.
 3. The appliance of claim 1, wherein the at least onecavity comprises a plurality of protrusions.
 4. The appliance of claim3, wherein the plurality of protrusions are shaped such that each of theprotrusions are brought into contact with the received patient's toothwhen the appliances initially positioned on the teeth.
 5. The applianceof claim 1, wherein the cavity comprises two protrusions positioned tocontact substantially opposing sides of a received tooth as theappliance is initially positioned on the tooth.
 6. The appliance ofclaim 5, wherein the two protrusions are selected to reduce a tippingmovement of the tooth during repositioning.
 7. The appliance of claim 1,wherein the selected tooth movement comprises a buccal translation,lingual translation, mesial translation, distal translation, extrusion,or intrusion.
 8. The appliance of claim 1, wherein the selected toothmovement comprises a first, second, or third order root movement.
 9. Anorthodontic appliance, comprising: a shell appliance having teethreceiving cavities shaped to receive and position a patient's teeth, oneor more of the cavities shaped to apply a resiliently repositioningforce to move the patient's teeth from the current arrangement towardthe target arrangement, the shell comprising a first cavity having aprotrusion configured to apply a repositioning force to a patient'stooth corresponding to a selected tooth movement, the first cavityfurther comprising a modification to a portion of the shell selected tocompensate for an effect due to positioning of the protrusion in thecavity.
 10. The appliance of claim 9, wherein the effect comprises anunwanted distortion in a shape of the appliance when worn by thepatient.
 11. The appliance of claim 9, wherein the effect comprises anunwanted force vector applied to a received tooth by a surface of theappliance.
 12. The appliance of claim 9, wherein the modificationcomprises changing the shape or curvature of a surface of the appliance.13. The appliance of claim 9, wherein the modification compriseschanging a shape or curvature of a surface without removing of a portionof the appliance.
 14. The appliance of claim 9, wherein the protrusioncomprises an interior ridge comprising a groove that recesses toward aninner surface of the appliance.
 15. The appliance of claim 9, whereinthe protrusion comprises an exterior ridge comprising a grooveprotruding toward an exterior surface of the appliance.
 16. Theappliance of claim 9, wherein the protrusion comprises a dimpleprotrusion having a length substantially equal to a width.
 17. Theappliance of claim 9, wherein the protrusion is a hollow protrusion. 18.The appliance of claim 9, wherein the protrusion further comprises amaterial deposited therein.
 19. A method of treating a patient,comprising administering to the patient the appliance of claim
 9. 20. Asystem for repositioning a patient's teeth according to an orthodontictreatment plan, the system comprising: a plurality of appliances shapedto receive and resiliently reposition teeth through a plurality ofplanned successive tooth arrangements so as to move the patients teethalong a treatment path from an initial position toward a final position,the appliances having teeth receiving cavities and wherein the cavitiesof successive appliances have different geometries shaped to receive andreposition teeth from a first position to a successive position, atleast one appliance of the plurality comprising a cavity having aridge-shaped protrusion shaped and positioned in the cavity to apply arepositioning force to a patient's tooth corresponding to a selectedtooth movement.
 21. The system of claim 20, wherein the cavity comprisesonly a single protrusion.
 22. The system of claim 21, wherein the singleprotrusion is positioned on a buccal side or a lingual side of thecavity.
 23. The system of claim 20, wherein the cavity comprises aplurality of protrusions comprising at least two protrusions shaped andpositioned in the cavity such that each of the at least two protrusionsare brought into contact with the received patient's tooth when theappliances is initially worn by the patient.
 24. The system of claim 23,wherein the at least two protrusions are positioned to contactsubstantially opposing sides of a received tooth.
 25. The system ofclaim 23, wherein the at least two protrusions comprise a firstprotrusion positioned on a buccal side of the cavity and a secondprotrusion positioned on a lingual side of the cavity. 26 The system ofclaim 25, wherein the first protrusion and second protrusion arepositioned so as to apply a lingual or buccal translational force to areceived tooth.
 27. The system of claim 23, the at least two protrusionscomprising a first protrusion positioned at a distal interproximal areaof the cavity and a second protrusion positioned at a mesialinterproximal area.
 28. The system of claim 27, wherein the firstprotrusion and second protrusion are positioned so as to apply a mesialor distal translational force to a received tooth.
 29. The system ofclaim 23, wherein the at least two protrusions are positioned gingivallyso as to apply an extrusion force to a received tooth.
 30. The system ofclaim 23, wherein the at least two protrusions are positioned occlusallyso as to apply an intrusion force to a received tooth.
 31. The system ofclaim 20, wherein the selected tooth movement comprises a first, second,or third order root movement.
 32. The system of claim 20, wherein theplurality of appliances comprise a first appliance to reposition teethfrom an initial tooth arrangement to a first intermediate arrangement;at least one intermediate appliance to progressively reposition teethfrom the first intermediate arrangement to successive intermediatearrangements; and a final appliance to progressively reposition teethfrom a last intermediate arrangement toward a final arrangement.
 33. Thesystem of claim 20, wherein the planned successive arrangements arebased on models of the patient's teeth generated prior to starting theorthodontic treatment plan.
 34. A system for repositioning a patient'steeth according to an orthodontic treatment plan, the system comprising:a plurality of appliances shaped to receive and resiliently repositionteeth through a plurality of planned successive tooth arrangements so asto move the patients teeth along a treatment path from an initialposition toward a final position, the appliances having teeth receivingcavities and wherein the cavities of successive appliances havedifferent geometries shaped to receive and reposition teeth from a firstposition to a successive position, at least one appliance of theplurality comprising a first cavity having a protrusion configured toapply a repositioning force to a patient's tooth corresponding to aselected tooth movement, the first cavity further comprising amodification to a portion of the shell selected to compensate for aneffect due to positioning of the protrusion in the cavity.
 35. A methodfabricating an orthodontic appliance for repositioning a patient'steeth, comprising: receiving a model of a patient's dentition in atarget arrangement; generating an appliance based on the model, theappliance having teeth receiving cavities shaped such that when theappliance is worn by the patient the cavities of the appliance receivethe patient's teeth in their current positions and resilientlyrepositions the teeth toward the target arrangement, the appliancefurther comprising at least one tooth receiving cavity having aprotrusion configured to apply a repositioning force to a received toothcorresponding to a selected tooth movement.
 36. The method of claim 35,wherein the model comprises a digital model of the patient's dentition.37. A method of treating a patient according to a treatment plancomprising a plurality of planned successive tooth arrangements formoving teeth along a treatment path from an initial arrangement toward aselected final arrangement, the method comprising: providing a set oforthodontic appliances, the set comprising a plurality of appliancesshaped to move teeth at least partially along the treatment path, theset comprising at least one appliance having teeth receiving cavitiesand shaped to apply a resiliently repositioning force to move thepatient's teeth from the current arrangement toward the targetarrangement, the at least one appliance comprising a cavity having aprotrusion configured to apply a repositioning force to a patient'stooth corresponding to a selected tooth movement.